L1 · FoundationsNumbers & loops~4 min · 5 tests

Convert Decimal to Binary

Convert a non-negative integer to its binary string by repeated division by 2, without bin(). Understand why it takes O(log n) steps. Live tests.

The problem

Return the binary representation of the non-negative integer n as a string, without using bin() or format(). 0 → "0".

Examples

Example 1
Input
```
to_binary(10)
```
Expected output
```
'1010'
```
Example 2
Input
```
to_binary(1)
```
Expected output
```
'1'
```

+ 3 hidden tests on Submit.

Edge cases to ask about

Zero
Powers of two

Hints

0/3

How an interviewer scores this

0/9

1. Understand the problemRestate it, ask about edge cases and input size.
2. Write a brute-force solutionCorrect first, clever later.
3. Get the correct outputautoAll visible examples pass.
4. Analyse time complexityautoCommit to a Big-O in the Complexity Lab.
5. Analyse space complexityautoExtra memory, not the input.
6. Identify the bottleneckautoMeasure your code — where does it bend?
7. OptimiseUsually: a set or dict instead of a scan.
8. Explain why it worksSay it out loud to Solvi.
9. Test the edge casesautoSubmit passes every hidden test.

Python 3.13 · to_binary

def to_binary(n):
    """Binary string of n without bin()."""
    # Write your solution here
    pass

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Complexity Lab

What does this cost as n grows?

Interviewers score the analysis as much as the code. Commit to an answer first — then check it, and read why.

Time complexity of the optimal solution

Space complexity (extra memory)

Pick both to reveal the answer.

From brute force to optimal

The progression an interviewer wants to hear, one step at a time.

Approach	Time	Space	Idea
Repeated division by 2	O(log n)	O(log n)	Remainders give the bits from least significant up.

Walkthrough of the optimal approach (try it yourself first)

Divide by 2 repeatedly and collect the remainders — they are the bits from least significant to most, so reverse them at the end. n halves each time, giving log₂(n) steps.

bin(n)[2:] and f"{n:b}" are the built-ins.

Complexity: O(log n) time, O(log n) space. n halves each step, so there are about log₂(n) steps and bits.

Reveal the reference solution

def to_binary(n):
    if n == 0:
        return "0"
    bits = []
    while n:
        bits.append(str(n % 2))
        n //= 2
    return "".join(reversed(bits))

Follow-ups interviewers ask

Convert binary back to decimal.
Any base from 2 to 16.

Frequently asked interview questions

Core interview concepts, complexities, and follow-ups scored by hiring teams.

What is the time complexity of Convert Decimal to Binary in Python?

The optimal solution runs in O(log n) time and O(log n) auxiliary space. n halves each step, so there are about log₂(n) steps and bits.

What follow-up questions do interviewers ask about Convert Decimal to Binary?

Convert binary back to decimal. Any base from 2 to 16.